Hexagonal Prism Calculator
Calculate volume, surface area, and other properties of a regular hexagonal prism
Calculation Results
Enter hexagonal prism measurements to calculate all properties.
Side Length (a): units
Base Area (B): square units
Height (h): units
Volume (V): cubic units
Lateral Area (L): square units
Surface Area (S): square units
Base Perimeter (P): units
Hexagonal Prism Diagram
Hexagonal Prism Formulas
Key Properties
- Side Length (a): Length of one side of the hexagonal base
- Base Area (B): Area of the hexagonal base
- Height (h): Distance between the two hexagonal bases
- Volume (V): Space contained within the prism
- Lateral Area (L): Area of the six rectangular faces
- Surface Area (S): Total area including both hexagonal bases
- Base Perimeter (P): Perimeter of the hexagonal base
Calculation Formulas
- Base Area (B): B = (3√3/2)a² ≈ 2.59808a²
- Volume (V): V = B × h
- Lateral Area (L): L = 6a × h
- Surface Area (S): S = L + 2B
- Base Perimeter (P): P = 6a
Where: a = side length of hexagon, h = height of prism
Example Calculation
For a hexagonal prism with:
Side length (a) = 5 units, Prism height (h) = 8 units.Calculations:
- Base Area ≈ 2.59808 × 5² ≈ 64.952 units²
- Base Perimeter = 6 × 5 = 30 units
- Volume ≈ 64.952 × 8 ≈ 519.616 units³
- Lateral Area = 6 × 5 × 8 = 240 units²
- Surface Area ≈ 240 + (2 × 64.952) ≈ 369.904 units²
About Hexagonal Prisms
A hexagonal prism is a three-dimensional shape with two identical hexagonal bases connected by six rectangular lateral faces. It has 8 faces, 18 edges, and 12 vertices. When the hexagon is regular (all sides and angles equal), the prism is called a regular hexagonal prism.
Real-World Applications
- Architecture: Some unique buildings and structures use hexagonal prism shapes
- Engineering: Hexagonal nuts and bolts use this shape
- Nature: Honeycomb structures in beehives are hexagonal prisms
- Packaging: Some specialty packages use hexagonal prism shapes
Special Cases
- Regular Hexagonal Prism: All sides of the base are equal and all angles are equal
- Right Hexagonal Prism: Lateral faces are rectangles (as opposed to parallelograms)
- Uniform Hexagonal Prism: All edges are equal length (becomes a hexagonal trapezohedron)
Hexagonal Prism Components
Base Area (B)
B ≈ 2.59808a²
Prism Height (h)
Lateral Area (L)
L = 6ah
Surface Area (S)
S = L + 2B
Base Perimeter (P)
P = 6a
Volume (V)
V = B × h
How to Use the Hexagonal Prism Calculator
The Hexagonal Prism Calculator helps compute various properties based on input values. Here's how to use it:
1. Select Calculation Method
Choose what measurements you know:
- Side Length & Height - Enter the hexagon side and prism height
- Base Area & Height - When you know the base area
- Volume & Height - To find the side length
- Lateral Area & Height - To find the side length
2. Enter Your Values
Input positive numbers in the appropriate fields:
Example 1: Side Length = 5, Prism Height = 8
Example 2: Base Area = 64.952, Prism Height = 8
3. Get Results
The calculator will compute all properties:
- Side Length (a)
- Base Area (B)
- Prism Height (h)
- Volume (V)
- Lateral Area (L)
- Surface Area (S)
- Base Perimeter (P)
Practical Applications
- Calculate material needed for hexagonal structures
- Determine paint required for hexagonal prism-shaped objects
- Find storage capacity of hexagonal containers
- Solve geometry problems involving hexagonal prisms
Frequently Asked Questions
A hexagonal prism has two hexagonal bases and six rectangular faces, while a hexagonal pyramid has one hexagonal base and six triangular faces meeting at a point (apex).
A hexagonal prism has 8 faces - two hexagonal bases and six rectangular lateral faces.
Use the formula: a = √(V / (2.59808 × h)) where V is volume and h is height.